This paper develops a capacity model for sequential zone picking systems. These systems are popular internal transport and order-picking systems because of their scalability, flexibility, high-throughput ability, and fit for use for a wide range of products and order profiles. The major disadvantage of such systems is congestion and blocking under heavy use, leading to long order throughput times. To reduce blocking and congestion, most systems use the block-and-recirculate protocol to dynamically manage workload. In this paper, the various elements of the system, such as conveyor lanes and pick zones, are modeled as a multiclass block-and-recirculate queueing network with capacity constraints on subnetworks. Because of this blocking protocol, the stationary distribution of the queueing network is highly intractable. We propose an approximation method based on jump-over blocking. Multiclass jump-over queueing networks admit a product-form stationary distribution and can be efficiently evaluated by mean value analysis and Norton’s theorem. This method can be applied during the design phase of sequential zone picking systems to determine the number of segments, number and length of zones, buffer capacities, and storage allocation of products to zones to meet performance targets. For a wide range of parameters, the results show that the relative error in the system throughput is typically less than 1% compared with simulation.

Logistics, Material handling, Queueing theory, Warehousing,
Operations Research
Department of Technology and Operations Management

van der Gaast, J.P, De Koster, R.B.M. (René B.M.), Adan, I, & Resing, J.A.C. (Jacques A.C.). (2020). Capacity analysis of sequential zone picking systems. Operations Research, 68(1), 161–179. doi:10.1287/OPRE.2019.1885